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# Failure Criteria for anisotropic composites

## Failure Criteria for anisotropic composites

(OP)
Hi All,

I am new to forum. I am currently looking into failure criteria and in particular Tsai Wu and Hashin form.

I was wondering if anyone knew any good sources where I could understand these theories??

After a lot of Google search, Some of the sources give me the equation of Tsai wu as "≤ 1" while some show "≥ 1".. I am terribly confused

Any help would be highly appreciated

Thank You

### RE: Failure Criteria for anisotropic composites

You have to have a failure criterion to assess the importance of an applied stress. You can't do without one (even for metal).

Accordingly the simplest failure criterion is probably
failure_index = applied_tensile_stress / allowable_ultimate_tensile_strength
or perhaps
FI = σ1T / Ftu

If the value of FI is greater than or equal to 1 failure is predicted. If it is less than 1 then no failure is predicted. It is that simple.

Note that for this simple failure criterion, in terms of reserve factor RF = 1 / FI (or margin of safety MS = 1/FI - 1). There's a little bit of debate because it is usualy taken that an FI of 1.0 indicates failure but an RF of 1.00 (an MS of 0.00) does not.

Tsai-Wu and Hashin are just more complicated variants of this which can be used with orthotropic materials and a complicated stress state.

Stephen Tsai and Ed Wu (deceased) worked quite hard to come up with one equation which applies to any stress state and any orthotropic material. Hashin uses several separate failure indices depending on the type of failure being checked.

For reference Tsai-Wu is
FI = σ1 / σ1AT - σ1 / σ1AC + σ2 / σ2AT - σ2 / σ2AC + σ12 / (σ1AT * σ1AC) + σ22 / (σ2AT * σ2AC) + τ122 / τ12A2 - σ1 * σ2 / Sqrt(σ1AT * σ1AC * σ2AT * σ2AC)

A = allowable.

In general Tsai-Wu when used with an isotropic material and when the equation is simplified accordingly boils down to von Mises with ultimate stresses and not yield.

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